When two transistors are cross-coupled by a dc path they may be used to create a flip-flop and, when properly cross-coupled by an R-C network, they may be used to create a multivibrator whose frequency of oscillation is determined by the R-C network's time constant. If the charging time of the capacitor can be varied by changing the input voltage a so-called voltage-controlled oscillator results. Instead of an R-C network, an LRC tank circuit may used to establish the frequency of oscillation and a crystal may be used to provide enhanced stability. To sustain oscillation, a transistor amplifier may be used to provide sufficient negative resistance to match the internal positive resistance of the tank circuit. If the tank circuit is in the feedback path its series resonant frequency is of principal importance in establishing the frequency of oscillation. However the crystal may be in either parallel or series resonance with the input impedance of the first stage, each mode generating a different frequency. See, for example, A Handbook of Piezoelectric Crystals for Radio Equipment Designers, Wright Air Development Center, Wright-Patterson Air Force Base, Ohio, July 1957, pp. 218-222. In addition, the feedback transistor's transconductance can not be too high or the oscillations may build up exponentionally and unpredictably from any noise input. Accordingly, oscillation build-up must be controlled.
As disclosed in an article entitled A High-Performance Crystal Oscillator Circuits: Theory and Application by Eric A. Vitoz and Marc G. R Degrauwe, IEEE Journal of Solid-State Circuits, vol. 23, no. 3, June 1988, pp. 774-782, a crystal may be represented by an equivalent electrical circuit in which each possible mode (i) of mechanical oscillation corresponds to a resonant circuit with the parameters L.sub.i, R.sub.i and C.sub.i having a motional impedance Zm.sub.i. To prevent undesired modes of crystal oscillation, the applied voltage must be maintained within appropriate limits.
There are several disadvantages to connecting the crystal at the input terminals of single transistor amplification stage with feedback. First, the voltage that is fed back to drive the crystal cannot exceed that of the battery supply voltage. Second, each side of the crystal sees a different circuit impedance so that any noise in the battery supply will be applied to the crystal tank circuit as a noise signal and will be amplified. These problems are partially alleviated by employing a two-transistor differential amplifier and by connecting the crystal between the inputs, or preferably, between the outputs of the two transistors. When the differentially connected transistors share a common constant current battery supply source any battery noise is cancelled. Moreover, when the crystal is connected between the differential outputs it may be subjected to maximum battery drive first in one direction and then in the other, thereby effectively experiencing twice the voltage swing of the single-transistor connection. While the differentially-connected, crystal- controlled multivibrator is an efficient and useful circuit, in certain applications, such as in hand-held radiotelephones where battery voltage may vary and power consumption must be minimized, it is important to rapidly bring the crystal tank circuit into an appropriate mode of oscillation when the circuit is turned on and then to sustain oscillation in that mode without overdriving the crystal and wasting power.